Title of the course: Minimal Submanifolds, Mean Curvature Flow and Isotopy Problems
Instructor: Andreas Savas-Halilaj
Institution: University of Ioannina
Dates: 13-19 January 2020
Prerequisites: Differential Geometry, Riemannian Geometry.
Level: Graduate
Abstract: Many fundamental results in geometry and topology have been established through the development of minimal submanifold theory and geometric flow techniques. In this mini course, I will start by discussing minimal submanifolds and scalar/vectorial maximum principles for elliptic and parabolic PDEs. Then, I will use these tools to prove Bernstein type theorems for graphical minimal submanifolds. Finally, I will focus on the mean curvature flow in high codimensions and will demonstrate how to use this powerful method to derive topological results for maps between Riemannian manifolds.
Textbook:
1. K. Smoczyk, Mean curvature flow in higher codimension: introduction and survey. Springer Proceedings in Mathematics, Vol 7, 231-274 (2012). Text also available on arXiv 1104.3222.
2. Y.-L. Xin, Minimal submanifolds and related topics, Nankai Tracts in Mathematics, Vol. 16 (2018).
Language: EN